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Results tagged with lie-algebras
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user 4213
Lie algebras are algebraic structures which were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used. Related mathematical concepts include Lie groups and differentiable manifolds.
9
votes
Root systems and sums of squares
If a quadratic form in $n$ variables is the sum of the squares of
$n$ integer linear forms, it's the sum of the squares of $n$ rational linear forms.
Thus it's equivalent
as a rational quadratic form …
- 20.8k
4
votes
Accepted
reductive Lie subalgebra
Sorry, this started as a comment, but got too long.
If $G$ is semisimple, then every derivation of $G$ is inner, so
that the normalizer $N_L(G)=C_L(G)+G$ where $C_L(G)$
is the centralizer. In this si …
- 20.8k
4
votes
Accepted
Reductive Lie algebra
A reductive Lie algebra $L$ is the direct sum of a semisimple
Lie algebra $L_1$ and an abelian Lie algebra $L_2$. Let's consider
the case where $L_2$ is one-dimensional.
We can embed $L$ into a larger …
- 20.8k
4
votes
Exceptional Lie algebras
I expect if you did construct a Lie algebra with relations built
from a "forbidden" Cartan matrix then you would get an infinite-dimensional
Kac-Moody algebra or something similar.
Also for the excep …
- 20.8k